Math
Hyperbolas.
Definition
A conic section formed by the set of all points where the absolute difference of distances to two fixed points (foci) is constant. A hyperbola has two separate curved branches that open either horizontally or vertically, with asymptotes guiding their shape.
Examples
Real-world.
- 1 The path of a spacecraft doing a gravitational slingshot around a planet
- 2 The shape formed by the shadow of a lampshade on a wall
- 3 LORAN navigation systems use intersecting hyperbolas to determine position
Key Fact
Standard form: (x−h)²/a² − (y−k)²/b² = 1 (horizontal) or (y−k)²/a² − (x−h)²/b² = 1 (vertical)